The sloshing phenomena in a two-dimensional rectangular tank are investigated using a level set method based on finite volume method. The code validations are performed by comparing between the present results and previous numerical results, which gives a good agreement. We present the streamlines pattern, free surface shape, maximum free surface elevation and pressure fluctuation patterns in the tank under the pitch and surge motions with various frequencies. These two different motions cause the different flow structures in the tank. The time variations of surface elevation and pressure at the different locations in the tank strongly depend on the exciting frequency of tank moving.